The usual "Delta method" for approximating the variance of a function of random variables, based on the first two terms of a Taylor series expansion, is well known. Sometimes, however, the resulting approximation is poor or zero. Less well known is the fact that a better approximation can be obtained by taking a further term in the Taylor series expansion. We have given the general formulation for this better approximation and illustrated its use in a situation where the usual delta method breaks down, namely in determining the variance of an estimate of heterozygosity and the PIC (polymorphism information content) value. These measures are important in determining how useful a genetic marker is for linkage analysis. In the case of heterozygosity, the variance by a second degree Taylor series approximation is the same as the exact variance. In the case of the PIC value, a numerical comparison was made between the approximate variance and the exact variance.